Multicomponent lattice Boltzmann equation method with a discontinuous hydrodynamic interface

In the multicomponent lattice Boltzmann equation simulation method (MCLB), applied to the continuum regime of fluid flow, the finite width of the fluid-fluid interface introduces unphysical scales. We present a practical, robust, computationally efficient, and easy to implement solution to this problem which needs only low order interpolation to be stable and accurate and is applicable to any MCLB variant which uses a continuous phase field to distinguish between immiscible fluids with arrested coalescence. Our method extends the ideas of Kim and Pitsch, [Phys. Fluids 19, 108101 (2007)] and uses no external force distribution whatsoever to generate continuum interfacial physics, i.e., the Laplace law and no traction conditions on interfacial stresses. As such, it is amenable to the simplest form of Chapman-Enskog analysis used for lattice Boltzmann models. We assess our method and proceed to compare key results obtained with it against other equivalent data, obtained using the established continuum regime MCLB technique based upon the work of Lishchuk, Care, and Halliday, [Phys. Rev. E 67, 036701 (2003)] and Halliday, Hollis, and Care, [Phys. Rev. E 76, 026708 (2007)], quantifying performance in terms of the minimum feasible capillary available to simulation using that technique.